Is there an Edge Detection Method that performs significantly better than the Canny Edge Detector ??
There are different types of "edges", it depends on your task. Have a look at the recent paper "Which edges matters?" from ICCV-2013, with comparison of several methods:
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ultrametric contour map - "Contour Detection and Hierarchical Image Segmentation" by P. Arbelaez, M. Maire, C. Fowlkes, and J. Malik - best results in comparison above.
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normalized cuts - "Normalized cuts and image segmentation" by J. Shi and J. Malik.
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mean shift - "Mean shift: A robust approach
toward feature space analysis" by D. Comanicu and P. Meer.
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Felzenszwalb and Huttenlocher approach - "Efficient graph-based
image segmentation" by Felzenszwalb and Huttenlocher.
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BiCE - "Binary coherent edge descriptors" by C. L. Zitnick.
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N4-Fields - "N4-Fields: Neural Network Nearest Neighbor Fields for Image Transforms" by Ganin et.al
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RDS - "Learning relaxed deep supervision for better edge detection" by Liu and Lew
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COB - "Convolutional Oriented Boundaries" by Maninis et.al.